R² (coefficient of determination)

share of the variation the model explains

R² = 1 − SS_residual / SS_total

The proportion of the variation of the response that the regression or DOE model explains, from 0 to 100 %. Adjusted R² corrects for the number of terms, so it does not rise just because more X columns are added.

A high R² does not prove cause and effect, and a low R² can still go with a significant, useful effect when the process is noisy.

Calculate it

Regression and Correlation: Simple and multiple regression, correlation, R², p-values and residual plot.

Related terms

• Correlation coefficient (Pearson r): strength of a straight-line relationship
• Residuals: what the model does not explain